CORRECTION OF SIGMA-DELTA ANALOG-TO-DIGITAL CONVERTERS (ADCs) USING NEURAL NETWORKS

ABSTRACT

Systems and methods for correction of sigma-delta analog-to-digital converters (ADCs) using neural networks are described. In an illustrative, non-limiting embodiment, a device may include: an ADC; a filter coupled to the ADC, where the filter is configured to receive an output from the ADC and to produce a filtered output; and a neural network coupled to the filter, where the neural network is configured to receive the filtered output and to produce a corrected output.

FIELD

This disclosure relates generally to electronic circuits, and morespecifically, to systems and methods for correction of sigma-deltaanalog-to-digital converters (ADCs) using neural networks.

BACKGROUND

In electronics, an analog-to-digital converter (ADC) is a system thatconverts an analog signal, such as a sound picked up by a microphone orlight entering a digital camera, into a digital signal. An ADC may alsoprovide an isolated measurement such as an electronic device thatconverts an input analog voltage or current to a digital numberrepresenting the magnitude of the voltage or current.

There are several ADC architectures. Due to the complexity and the needfor precisely matched components, all but the most specialized ADCs areimplemented within integrated circuitry. These may take the form ofmixed-signal integrated circuits (“ICs”) that integrate both analog anddigital circuits.

More specifically, an ADC converts a continuous-time andcontinuous-amplitude analog signal to a discrete-time anddiscrete-amplitude digital signal. The conversion involves quantizationof the input, so it necessarily introduces a small amount of error ornoise. Furthermore, rather than continuously performing the conversion,an ADC does the conversion periodically, sampling the input, thuslimiting the allowable bandwidth of the input signal.

The performance of an ADC is primarily characterized by its bandwidthand signal-to-noise and distortion ratio (SNDR). The bandwidth of an ADCis characterized primarily by its sampling rate. The SNDR of an ADC isinfluenced by many factors, including one or more of: resolution,linearity, accuracy (how well the quantization levels match the originalanalog signal), aliasing, or jitter.

During the design, layout, and manufacturing of ICs, many errors may beintroduced in an ADC. In the design phase, for example, errors may beintroduced due to the non-linearity of the circuit components. ADCs maysuffer from nonlinearity errors caused by their physical imperfections,resulting in their output deviating from a linear function (or someother function, in the case of a deliberately nonlinear ADC) of theirinput. These errors can sometimes be mitigated by calibration orprevented by testing. Important parameters for linearity are integralnonlinearity and differential nonlinearity. These nonlinearitiesintroduce distortion that can reduce the SNDR ratio performance of theADC and thus reduce its effective resolution. Errors may also beintroduced in the layout phase due to unwanted parasitic effects.Moreover, during the manufacturing phase, errors may be introduced bymismatches in components, which can lead to additional non-linearitiesas well as offset and gain errors.

To correct these errors, a typical approach is to increase the layoutarea and power of the circuits in the ADC, and to spend considerablehours optimizing circuit designs and layouts, which is a very tediousprocess.

Another approach for correcting ADC errors is calibration.Unfortunately, a calibration approach for each different type of erroris often required, which is accompanied by significant mathematicalanalysis and modeling, while also incurring an increase in hardware, andtherefore area and cost. If different calibration methods are combined,convergence issues of different calibration loops might occur, leadingto even more complexity.

In the measurement instrument and sensor markets, a crucial role isplayed by ADCs, which today represent a core of most digital equipment.Consequently, the operation of ADCs strongly affects the overallperformance of the measurement or sensor apparatuses in terms of theirmetrological accuracy. To increase the performance of such instruments,it may be important either to design new ADCs with improved linearityand accuracy, or to develop suitable techniques for compensating for ADCerrors.

BRIEF DESCRIPTION OF THE DRAWINGS

The present invention(s) is/are illustrated by way of example and is/arenot limited by the accompanying figures, in which like referencesindicate similar elements. Elements in the figures are illustrated forsimplicity and clarity and have not necessarily been drawn to scale.

FIG. 1 is a block diagram of an example of a first system for correctinga sigma-delta analog-to-digital converter (ADC), shown in a trainingconfiguration, according to some embodiments.

FIG. 2 is a block diagram of an example of the first system operatingduring an inference phase, according to some embodiments.

FIG. 3 is a graph of an example of an uncorrected sigma-delta ADC outputsignal, according to some embodiments.

FIG. 4 is a graph of an example of a corrected sigma-delta ADC outputsignal produced by the first system, according to some embodiments.

FIG. 5 is a block diagram of an example of a second system forcorrecting a sigma-delta ADC, shown in a training configuration,according to some embodiments.

FIG. 6 is a block diagram of an example of the second system operatingduring an inference phase, according to some embodiments.

FIG. 7 is a graph of an example of a corrected sigma-delta ADC outputsignal produced by the second system, according to some embodiments.

FIG. 8 is a block diagram of an example of a third system for correctinga sigma-delta ADC, shown in a training configuration, according to someembodiments.

FIG. 9 is a block diagram of an example of a fourth system forcorrecting a sigma-delta ADC, shown in a training configuration,according to some embodiments.

DETAILED DESCRIPTION

Embodiments described herein provide systems and methods forcompensating or correcting the output of analog-to-digital converters(ADCs), particularly delta-sigma ADCs, using neural networks. In variousimplementations, systems and methods described herein may significantlyreduce one or more of: (i) an ADC's hardware complexity, by avoiding therequirements for mathematical analysis of each error; (ii) the need foran accurate error model to enable calibration (an error model would berequired for each parameter to be calibrated, which may complicatecalibration); or (iii) the need to implement circuitry usable tocalibrate for analog circuit errors.

Generally, the addition of circuit elements to an ADC's analog circuitrywould come at the cost of ADC performance because additional parasiticswould be introduced. In contrast, systems and methods described hereinmay not require additional analog circuits to be added to an ADC, andtherefore the ADC's performance is not compromised; to the contrary, itmay be increased. Particularly, increased area for additional circuitsis not needed to improve matching, and electrical current does not haveto be increased to improve linearity. Moreover, if multiple parametersneed to be calibrated, traditional calibration approaches might requirea substantial increase in additional analog circuits to enable suchcalibration, whereas systems and methods described herein do not requireadditional analog circuits for calibration. Instead, digital hardwareand a representative data set may be added.

Various disclosed embodiments disclosed herein may include one or morefeatures such as, for example: (i) a direct feed of data from an ADCwithout a need for storage between the ADC and a neural network; (ii) areduction of input word width from the ADC to the neural network withoutperformance loss; and (iii) and the inclusion of process information toenable the neural network system to compensate for processes variations(e.g., temperature/voltage drifts and process shifts). In some cases, anADC may be designed such that it has sufficiently low circuit noise,without necessarily optimizing it for non-linearities or other errors,and instead systems and methods described herein may utilize a neuralnetwork or other machine learning mechanisms to compensate for all sucherrors.

As used herein, the term “machine learning” refers to one or morealgorithms that implement: a neural network (e.g., artificial neuralnetwork, deep neural network, convolutional neural network, recurrentneural network, autoencoders, reinforcement learning, etc.), fuzzylogic, artificial intelligence (Al), deep learning, deep structuredlearning hierarchical learning, support vector machine (SVM) (e.g.,linear SVM, nonlinear SVM, SVM regression, etc.), decision tree learning(e.g., classification and regression tree or “CART,” ensemble methods(e.g., ensemble learning, Random Forests, Bagging and Pasting, Patchesand Subspaces, Boosting, Stacking, etc.), dimensionality reduction(e.g., Projection, Manifold Learning, Principal Components Analysis,etc.), or the like.

Non-limiting examples of publicly available machine learning algorithms,software, and libraries that may be utilized within embodiments ofsystems and methods described herein include, but are not limited to:PYTHON, OPENCV, INCEPTION, THEANO, TORCH, PYTORCH, PYLEARN2, NUMPY,BLOCKS, TENSORFLOW, MXNET, CAFFE, LASAGNE, KERAS, CHAINER, MATLAB DeepLearning, CNTK, MatConvNet (a MATLAB toolbox implementing convolutionalneural networks for computer vision applications), DeepLearnToolbox (aMatlab toolbox for Deep Learning from Rasmus Berg Palm), BigDL,Cuda-Convnet (a fast C++/CUDA implementation of convolutional orfeed-forward neural networks), Deep Belief Networks, RNNLM,RNNLIB-RNNLIB, matrbm, deeplearning4j, Eblearn.lsh, deepmat, MShadow,Matplotlib, SciPy, CXXNET, Nengo-Nengo, Eblearn, cudamat, Gnumpy, 3-wayfactored RBM and mcRBM, mPoT, ConvNet, ELEKTRONN, OpenNN,NEURALDESIGNER, Theano Generalized Hebbian Learning, Apache SINGA,Lightnet, and SimpleDNN.

Various systems and methods disclosed herein are described with respectto utilization of an artificial neural network (also simply referred toherein as a “neural network”). However, a person of ordinary skill inthe art may choose to implement other appropriate machine learningsystems, such as previously disclosed, for compensating for ADC errors,in accordance with embodiments of the present disclosure.

A neural network is typically based on a collection of connected unitsor nodes referred to as artificial neurons, which loosely model theneurons in a biological brain. Each connection, like the synapses in abiological brain, can transmit a signal to other neurons. An artificialneuron receives a signal, processes it, and communicates results toother neurons connected to it. In neural network implementations, the“signal” at a connection is a real number, and the output of each neuronis computed by some non-linear function of the sum of its inputs. Theconnections are referred to as edges. Neurons and edges typically have aweight that adjusts as training of the neural network proceeds. Theweight increases or decreases the strength of the signal at aconnection. Neurons may have a threshold such that a signal is sent onlyif the aggregate signal crosses that threshold.

Typically, neurons are aggregated into layers. Different layers mayperform different transformations on their inputs. Signals travel fromthe first layer (the input layer) to the last layer (the output layer),possibly after traversing the layers multiple times. A neural networkarchitecture may be configured as a feed-forward network with one ormore hidden layers, and with a backpropagation learning algorithm.

Implementation of a neural network may involve three phases: a trainingor learning phase, a validation phase, and an inference or productionphase. In the training phase, the neural network essentially learns bycomparing its actual output with correct outputs (or at least outputsthat are nearer a desired output) to find errors. It then modifies themodel accordingly. In the validation phase, the trained neural networkis verified by means of data (“validation set”), which may be differentfrom the data used in the training phase. In the inference or productionphase, the trained and validated neural network is now configured andcapable of providing outputs that correspond to any input.

In various embodiments, systems and methods described herein may provideADC circuitry that implements an ADC in combination with a neuralnetwork that has been trained to learn what an ADC's errors are, and tolearn how to compensate for the errors. As referred to herein, ADCerrors may be any type of distortion caused by circuitry within an ADCthat results in its digital output signal not being a true or “ideal”digital conversion of the input analog signal. Such analog-to-digitalconversion errors may be caused by non-linearities within the ADCcircuitry, or any other defects or processing parameters that canproduce such ADC errors, which may take the form of noise, distortion,harmonics, etc.

Generally, an ADC may be any type of ADC implemented within any type ofdevice or circuitry that utilizes an ADC. In many implementations,however, an ADC as described herein may be a sigma-delta ADC. As usedherein, the term “delta-sigma ADC” generally refers to an ADC thatincludes, in addition to some analog circuitry, an oversampling (or“sigma-delta”) modulator followed by a digital/decimation filter thatproduces a digital data stream output.

In a sigma-delta ADC, the sigma-delta modulator uses noise shaping toreduce the quantization noise in a particular band anywhere between 0and fs/2, where “fs” is its sampling rate. Noise shaping lowers thein-band quantization noise to result in a high signal-to-noise ratio(SNR) in the signal bandwidth. The shaped quantization noise, which isout-of-band, may be eliminated by the decimation filter that comes afterthe sigma-delta modulator.

The use of a neural network as a post-correction stage involves theneural network storing “anti-errors” in the neural network. In case ofdistortion caused by non-linearity of the circuitry in the ADC, theneural network during training learns a non-linear function to correctfor that distortion; that is, the neural network operates as anon-linear transfer function.

In Nyquist ADCs, certain of the techniques described herein may be usedas a post-correction stage, because usually Nyquist converters have awhite noise floor (noise density is frequency independent between0-fs/2) and back-and-forth folding is not an issue (unless there areother signals in the spectrum that should not fold). In sigma-deltaADCs, however, this is not the case. Although non-linearity in theneural network may be used to correct for distortion of the ADC'ssigma-delta modulator, the same non-linearity may also cause fold-backof quantization noise back to the signal bandwidth, thus making thenoise shaping less effective.

In the figures that follow, neural networks may be implemented with anytype of hardware and/or software (as will be further disclosed herein),such as within an appropriate set of digital circuitries suitable forimplementation of a neural network. The illustration of neural networkswithin the figures is not to be limiting upon the scope of embodimentsof the present disclosure. Within the various figures, “(A)” representsthat the signal is an analog signal, and “(D)” represents that thesignal is a digital signal.

FIG. 1 is a block diagram of an example of a first system for correctingdevice-under-test (DUT) sigma-delta ADC 101, here shown in a trainingconfiguration. In various embodiments, DUT sigma-delta ADC 101 may havean internal delta-sigma modulator in series with a digital filter. Assuch, DUT sigma-delta ADC 101 may use noise shaping to shape thequantization noise of a low bit-count quantizer to higher frequencies.

Because of the low bit-count quantizer, however, significantquantization noise may be introduced. The internal digital filter mayshape the quantization noise to moved most of it out of the signalbandwidth. Although the internal digital filter's shaping reducesin-band noise, it also increases noise outside the signal band ofinterest, which would ordinarily cause a problem in neural networkpost-correction: due to non-linearity, the out-of-band quantizationnoise folds back into the signal's band. For example, second and thirdorder distortion causes intermodulation (e.g., intermodulation products)of out-of-band quantization noise, causing quantization noise to foldback into the signal bandwidth.

To avoid this fold back, filter G 106 may be coupled between the outputof DUT sigma-delta ADC 101 and neural network 102. The output of DUTsigma-delta ADC 101 (or any other ADC that has significant out-of-bandfrequency content) is filtered by filter G 106. Any noise or otherout-of-band frequency content may be reduced or removed by filter G, toa level where no significant quantization noise or out-of-band signalcontent fold back occurs, and to a level where the learning process ofneural network 102 is not significantly disturbed.

Filter G 106 may be a finite impulse response (“FIR”) filter or aninfinite impulse response (“IIR”) filter. Filter G 106 may be alow-pass, bandpass, or high-pass filter, depending on the input signalused during the training phase. The gain of filter G 106 may be selectedat the training frequency (or frequencies). In the case of a sine waveinput, filter G 106 may be configured to pass the fundamental harmonicof the input signal, and to block all higher order harmonics. Thefunction of filter G 106 may be changed depending on the frequency ofthe input signal and harmonics. For example, if the frequency of theinput signal is reasonably high, a bandpass filter may be used to removethe low and high frequency noise and the signal harmonics. Filter G 106may be a programmable filter that would be configured to allow for afrequency dependent training of the neural network 102.

During a training phase, a representation of an output from referenceADC 103 (labeled “target signal”) may be used to train neural network102 for compensation of the output signal of DUT sigma-delta ADC 101.The target signal may be provided by hardware-implemented reference ADC103 also receiving the same analog input signal (or an equivalentdigital input signal) as DUT sigma-delta ADC 101. If reference ADC 103is also a sigma-delta ADC, it may also be coupled to filter H 107.Moreover, if DUT sigma-delta ADC 101 and reference ADC 103 have the sameout-of-band quantization noise error, filters G 106 and H 107 may bedifferent instances of the same filter.

Hardware implemented reference ADC 103 may be pre-selected as known tobe substantially accurately calibrated (e.g., with a desired minimum setof errors in converting an analog signal to a digital signal, or atleast fewer errors than produced within DUT sigma-delta ADC 101). Theequivalent digital input signal may be configured to be a representationof an output of a reference ADC without errors (or with fewer errorsthan DUT sigma-delta ADC 101). If it is known that the DUT sigma-deltaADC 101 and reference ADC 103 have different propagation delays,appropriate circuitry may be added to compensate for such differences.

Neural network 102 may be trained using error signals, which are thedifferences between corrected output signals from neural network 102 andthe target signal. To accomplish this, the target signal is subtractedfrom the corrected output signal of neural network 102 using acomparator, or the like. The error signal produced is passed throughcost function 104 used to train neural network 102 (e.g., usingbackpropagation or similar algorithms). Backpropagation computes thegradient in weight space of a feedforward neural network, with respectto a loss function. Using backpropagation, computational parameters(e.g., weights and/or biases) of neural network 102 are adapted (e.g.,following a steepest descent method, also known as gradient descent).However, other suitable cost functions and training algorithms may beutilized for training the neural network.

The training phase may be continuously, or repeatedly, performed untilthe corrected output signal of neural network 102 has minimum errors (orat least a desired set of fewer errors) as compared to the target signalafter completion of the training phase. One manner by which the errorcan be measured is with a Fast Fourier Transform (FFT) to checkdistortion in the spectrum of the corrected output signal.Alternatively, a cost output may be used to determine when the error isreduced to an acceptable level.

Whenever hardware implemented reference ADC 103 is too expensive to beimplemented on-chip or too cumbersome to have available at final test,it may be replaced by a digital input signal for use as the targetsignal. The digital input signal is synchronized with the analog inputsignal. The digital input signal may be selected to represent an outputfrom a reference ADC that contains fewer analog-to-digital conversionerrors (e.g., due to non-linearities or other forms of distortion) thanDUT sigma-delta ADC 101. The digital input signal may also be selectedso that the error signal does not become too large for the trainingphase to adjust the weights and biases of neural network 102 efficientlyor satisfactorily.

Training of the neural network 102 can be performed under differentscenarios. For example, the training phase may be performed for eachindividual DUT sigma-delta ADC 101 (e.g., for each integrated circuit or“IC” containing DUT sigma-delta ADC 101, or separately for each ofmultiple ADCs implemented on a single IC). This approach yields a neuralnetwork specifically trained for each DUT sigma-delta ADC. Because ofvariations in the manufacturing of each individual ADC, training ofneural network 102 for a given ADC may not work equally well for anotherADC, and in such instances, the other ADC may be at least partiallyre-trained.

In some cases, the training phase can be performed on a batch ofmultiple DUT sigma-delta ADCs (e.g., on multiple ICs, each containing aDUT sigma-delta ADC). In this way, trained neural network 102generalizes errors into one model; i.e., the neural network knowledgebase after training. Such a knowledge base is representative of allerrors present in the batch of multiple ADCs, and it may represent andcompensate for errors that generalize well across multiple ADCs.

In other implementations, one or more Process-Voltage-Temperature (PVT)parameters 105 may be optionally incorporated so that the neural network102 can further compensate the output of DUT sigma-delta ADC 101.

Process variation accounts for deviations in semiconductor fabricationprocesses. These process variations may be due to variations in themanufacturing conditions, such as temperature, pressure, and dopantconcentrations. Voltages (e.g., supply voltage, reference voltage, biascondition on a device) utilized within an IC can vary from theestablished designed value during day-to-day operation and over itslifetime, which can affect the operation of circuit components in anADC. And, when an IC is operating, the temperature can vary throughoutthe IC, which affects the operational parameters of various circuitcomponents.

For example, analog circuits, such as implemented for incorporation ofADCs, are known to be voltage and/or temperature dependent. Accordingly,in some cases, voltage-temperature (VT) corner information may beprovided to neural network 102 as an input to enable neural network 102to correct for voltage and/or temperature drifts that can cause errorsin the operation of DUT sigma-delta ADC 101, so that neural network 102can further compensate for such voltage and/or temperature drifts.

Moreover, temperature and voltage information are often readilyavailable on ICs. For example, an IC where DUT sigma-delta ADC 101 isimplemented may include temperature and/or voltage sensors whose outputscan be input into neural network 102 along with the output of DUTsigma-delta ADC 101. As a result, when neural network 102 is trained,cost function 104 accounts for the effects on the errors caused by suchprocessing inputs to be utilized for adjusting the weights and biaseswithin the nodes of neural network 102.

Other types of process-related information may be added as a PVT Inputto neural network 102, such as various technology parameters (e.g.,electron mobility, transistor parameters (e.g., Vt, fT, Beta, doping),resistor parameters (e.g., nominal resistor value, voltage dependency),or capacitor parameters (e.g., nominal capacitor value, voltagedependency). If there is a way to measure a process-related parameter,then the output of this measurement can be provided as a PVT Input toneural network 102.

Even if a particular PVT parameter cannot be measured on the IC, so longas it may be obtained from wafer measurements, the PVT parameter may bestored in a memory device (not shown) on the IC or supplied from anexternal source (e.g., an external memory device or a microprocessor ormicrocontroller) as a digital PVT input into neural network 102.Furthermore, neural network 102 may be trained based on all availablePVT parameters or any desired subset of one or more PVT parameters for aparticular ADC or a batch of ADCs.

In a validation phase following the training phase, an analog inputsignal may be input to DUT sigma-delta ADC 101 and reference ADC 103 tocheck if the error is now sufficiently small or at least reduced for aset of inputs that DUT sigma-delta ADC 101 may encounter. In some cases,the validation phase may be utilized on one or more batches of ADCs todetermine if another batch of ADCs would be satisfactorily compensatedby a trained neural network 102. Moreover, if neural network 102 wastrained with one or more PVT parameters 105 or signal(s), these mayagain be utilized in the validation phase.

The validation process may check whether neural network 102 has properlylearned to correct the non-linearity of DUT sigma-delta ADC 101. One ormore input signals may be provided to DUT sigma-delta ADC 101 and toreference ADC 103, the output of filter G 106 as processed by neuralnetwork 102 is compared to the output of filter H 107, and the errorsignal is monitored. The output signal and the target signal (D) shouldbe properly aligned to prevent the error signal from containing too muchinput signal. Additionally, or alternatively, one or more input signalsmay be provided to DUT sigma-delta ADC 101, and, through an FFT, it isjudged if the output signal of neural network 102 is good enough (e.g.,by looking at the distortion/intermodulation or noise floor). In thatcase, reference ADC 103 (or any other target signal source), filter H107, and cost function 104, are not needed.

In some cases, such as when the training of DUT sigma-delta ADCs 101 isperformed in a single sample training process (not in batches of ADCs),the validation phase may be omitted, and the inference phase describedbelow may be sufficient.

FIG. 2 is a block diagram of an example of the first system operatingduring an inference phase. In some embodiments, FIG. 2 illustrates theinference or production phase whereby the ADC circuitry (i.e., DUTsigma-delta ADC 101, filter G 106, and neural network 102) areimplemented (e.g., on an IC) for operation within a final end-useapplication (e.g., the end-use application of the IC).

During the inference phase, an analog input signal may be applied to DUTsigma-delta ADC 101, which produces a digital output signal filtered byfilter G 106 and then modified by trained neural network 102 to producea compensated or calibrated corrected output signal (which may beutilized by another circuit within the IC).

The inference phase of FIG. 2 may also be utilized for the finalproduction testing of trained neural network 102. For example, theoutput of neural network 102 may be checked by comparing it tospecification parameters of the sigma-delta ADC 101. In addition, asdescribed with respect to FIG. 1 , training neural network 102 may beoperated to account for one or more PVT parameters 105 during theinference phase.

It should be noted that, during the inference phase, the presence offilter G 106 is still required to avoid out-of-band quantization noiseto fold back. In any of the three phases mentioned above, however,filter G 106 may alternatively be implemented as part of the sigma deltaADC's internal decimation filter. Additionally, or alternatively, thedecimation itself (i.e., sample rate reduction) may be performed justafter filter G 106 (in this case, filter G 106 is the decimation filter)or just after neural network 102. Finally, the training of neuralnetwork 102 may be performed while sigma-delta ADC 101 is being used inthe inference phase; during operation, a proper target signal may beprovided for training.

FIG. 3 is a graph of an example of uncorrected sigma-delta ADC outputsignal 300. In uncorrected signal 300, the Total Harmonic Distortion(THD) is −51 dB and the SNR at 3 kHz is 106 dB. In contrast, FIG. 4 is agraph of an example of corrected sigma-delta ADC output signal 400produced by the first system operating in inference mode, as shown inFIG. 2 . In corrected signal 400, the THD is −86 dB and the SNR at 3 kHzis 105.3 dB. As such, use of systems and methods described hereinimproved the THD of the ADC's output signal by about 35 dB while thenoise floor remained approximately the same. In many cases, results maybe further improved through more extensive training time.

In the first system, neural network 102 provides a fully corrected DUTsigma-delta ADC 101 output. A feature of such a system is that neuralnetwork 102 is configured to provide the full dynamic range of thecorrected DUT ADC. In contrast with this approach, however, is alsopossible for neural network 102 to predict only the error of a DUT ADC,which may then be subtracted from the uncorrected DUT ADC's output(e.g., using a comparator) to yield a corrected DUT ADC output. Toillustrated this, FIGS. 5 and 6 show a second system with less hardwarebeing required for neural network 102, as it is configured to predictonly the error.

FIG. 5 is a block diagram of an example of a second system forcorrecting DUT sigma-delta ADC 201, shown in a training configuration.In this embodiment, neural network 202 is trained by the differencebetween the filtered output signal of DUT sigma-delta ADC 201 (i.e.,without compensation by neural network 202), which may be performedusing a comparator, and the output of reference ADC 203. Thisdifference, here labeled a target signal, is then subtracted from apredicted error signal output of neural network 202, which is thenprocessed through cost function 204 to train neural network 202 (e.g.,using backpropagation or similar algorithms).

This approach for training of neural network 202 results in neuralnetwork 202 only needing to provide the error, and thus does not have toprovide the complete DUT sigma-delta ADC 201's dynamic range (or codes),which may require less hardware for implementation of neural network202, as fewer nodes are needed (because the errors made by DUTsigma-delta ADC 201 usually only span the lower significant bits or“LSBs” of the DUT sigma-delta ADC 201's output. Therefore, the outputword width (and internal calculation word widths) of neural network 202may be made smaller, since it is only compensating for the distortionwithin DUT sigma-delta ADC 201.

As described above, filter G 206 may be coupled between the output ofDUT sigma-delta ADC 201 and neural network 102 to prevent fold back. Ifreference ADC 203 is also a sigma-delta ADC, it may also be coupled tofilter H 207. One or more PVT parameters 205 may be incorporated so thatthe neural network 202 can further compensate the output signal of DUTsigma-delta ADC 201, to the extent PVT variations can cause errors inthe operation of DUT sigma-delta ADC 201. Incorporation of PVTparameters 205 or a digital PVT Input signal may be performed in amanner as similarly described with respect to FIG. 1 .

The training phase configuration of FIG. 5 may be applied to a singleADC or to a batch of ADCs. As in FIG. 1 , a digital input signalreplaces reference ADC 203, in which an equivalent digital input signalmay be configured to be a representation of an output of a reference ADCwith no errors, or at least fewer errors than DUT sigma-delta ADC 201.

During validation, an analog input signal is input to DUT sigma-deltaADC 201 and reference ADC 203 to check if the error is now sufficientlysmall or at least reduced for a set of inputs that DUT sigma-delta ADC201 is designed to encounter. The validation phase may be performed in amanner as similarly described above, for example using an FFT or thelike. Again, a validation phase may be utilized when training has beenperformed on one or more batches of ADCs to determine if another batchof ADCs would be also satisfactorily compensated by trained neuralnetwork 202. In some embodiments, reference ADC 203 may be replaced by adigital input signal.

In accordance with certain embodiments of the present disclosure, ininstances where training of ADCs is performed in a single sampletraining process (i.e., not in batches of ADCs), the validation phasemay be omitted, and the inference phase described below may besufficient. If the neural network 202 was trained with one or more PVTparameters 205, these may be utilized within the validation phase.

FIG. 6 is a block diagram of an example of the second system operatingduring an inference phase. In some embodiments, the configuration ofFIG. 6 may be used for the final production testing of DUT sigma-deltaADC 201 and within the end-use application of an IC in which DUTsigma-delta ADC 201 is implemented. Particularly, a predicted erroroutput from neural network 202 may be subtracted from the output signalof the DUT sigma-delta ADC 201 201, as filtered by filter G 206, toprovide a compensated, corrected output signal. In some cases, neuralnetwork 202 may be operated to account for PVT parameters 205 during theinference phase.

FIG. 7 is a graph of an example of corrected sigma-delta ADC outputsignal 700 produced by the second system, according to some embodiments.In corrected signal 400, the THD is also −86 dB, and the SNR at 3 kHz isstill 105.3 dB, compared to uncorrected signal 300 of FIG. 3 . Again, byusing systems and methods described herein, THD improved by about 35 dBwhile the noise floor remained approximately the same.

The performance of a compensated ADC (e.g., DUT ADC 101/201 combinedwith neural network 102/202) is not superior to that of a reference ADC(e.g., 103/203). Also, implementing a reference ADC on-chip maysometimes not be practical, insofar as doing so obviates the need for aDUT ADC and neural network in the first place, and would generallyrequire more area, power, and design time, than a lower performing ADCwith a neural network post-compensator (except when onehigh-performance, large area, high-power reference ADC is used tocalibrate multiple small area, low power DUT ADCs using neuralnetworks).

In some cases, to address these concerns, as an alternative approach thereference ADC may be disposed on a test board during final test.However, a high-performance reference ADC on a Printed Circuit Board(PCB) test board in a test environment can create interference issues.Furthermore, such an approach may also lead to other practical problemssuch as getting the reference ADC output bits into the chip under test,as it needs to connect to the neural network. Conversely, the DUT ADCmay come off the chip to enable off chip training of the neural network,and neural network parameters may be loaded on the chip under test aftertraining. Yet, when the ADCs are high resolution or high speed, thisalternative approach can produce additional issues, including the needfor many interfaces, and high-speed interfaces.

In some implementations, clock synchronization of the ADCs may also bean issue. The input signal of the reference ADC and DUT ADC should besynchronized. Due to parasitic poles on the PCB or on-chip, phasedifferences can occur, which can lead to errors in the constructed errorsignal fed to the back propagation algorithm. Furthermore, the DUT ADCand reference ADC both need the same high quality input signal.Connecting this signal in two different places may result in yetadditional challenges. For example, if the reference ADC were neededduring final test of a product, it would have to be placed to be on thetester load board where PCB space is expensive or unavailable.

To address these, and other concerns, additional embodiments may replacethe reference ADC (e.g., 103/203) with another digital filter. Thesecond digital filter (F) may be used to filter away the harmonics andexcessive noise coming from a DUT ADC, such that the DUT ADC's inputsignal may be reconstructed in the digital domain. The differencebetween the reconstructed sine wave output by the second filter and theDUT ADC output may be fed to the back propagation algorithm. To producea reconstructed reference signal, the second filter may be a low-pass,bandpass, or high-pass filter.

FIG. 8 is a block diagram of an example of a third system for correctingDUT sigma-delta ADC 301, shown in a training configuration. In thisembodiment, reference ADC 103/203 is replaced by filter F 309, whichfilters the output of filter G 306. To compensate for the delay infilter F 309, the signal from filter G 306 to neural network 302 isdelayed by ΔT using delay circuit 308, which may be configured with afixed delay or a frequency-dependent delay. In this way, the signalcoming out of neural network 302 is properly synchronized to the targetsignal. If filter F 309 cannot be connected to the output of filter G306, filter F 309 may instead be connected directly to the output of theDUT sigma-delta ADC 301. Also, one or more PVT parameters 305 may beincorporated so that neural network 302 can further compensate theoutput of DUT sigma-delta ADC 301.

Filter F 309 is used to substantially filter out the harmonics producedby DUT sigma-delta ADC 301 during conversion of the analog input signal,which reconstructs the input signal. Essentially, the output of thefilter F 309 represents an “ideal” digital signal that normally would beproduced by a reference ADC that produces fewer conversion errors thanDUT sigma-delta ADC 301. In other words, filter F 309 may be configuredto produce a sine wave at its output that sufficiently represents anoutput of a reference ADC that produces a desired amount of fewerconversion errors than DUT sigma-delta ADC 301. This can be done bydesigning the parameters of filter F 309 so that it filters out anamount of distortion (e.g., harmonics or excessive noise) that neuralnetwork 302 is to be trained to compensate for.

In some embodiments, a quantizer may be introduced after filter F 309 toreduce the amount of output bits, as filter F 309 may be long dependingon pass-band/stop-band requirements, leading to large word widths, andtherefore result in additional hardware implemented within neuralnetwork 302. Quantization, in digital signal processing, is a process ofmapping input values from a large set to output values in a (countable)smaller set, often with a finite number of elements. A quantizer may beany device that is configured to perform a desired quantization (e.g.,truncating, rounding, scaling, a highest number of bits, a lowest numberof bits, etc.). As such, one or more quantizers may be used throughoutthe system to limit word widths, thus saving hardware. In some cases, toreduce hardware cost, the number of bits coming out of filter G 306 mayalso be quantized.

It should be noted that filter G 306 may reduce requirements on filter F309, as filter G 306 already removes the out-of-band quantization noise,to negligible levels, and filter F 309 only needs to make sure harmonicsand possibly in-band noise is removed to create a good enough referencesignal for training. Furthermore, filters G 306 and F 309 both may beran at the ADC clock frequency or a decimator may be coupled to theoutput of filter G 306.

A validation phase may be performed similarly as previously described,where an analog input signal is provided to DUT sigma-delta ADC 301 tocheck if the error is now sufficiently small or at least reduced for aset of exemplary inputs that DUT sigma-delta ADC 301 may encounter.Where the training of ADCs is performed in a single sample trainingprocess (i.e., not in batches of ADCs), the validation phase may beomitted.

During an inference or production phase, components 304, 308, and 309may be removed, and the same configuration of FIG. 2 may be used. Duringthis inference phase, an analog input signal is applied to DUTsigma-delta ADC 301, which produces a digital output signal that is thenmodified by the trained neural network 302 to produce a compensated orcalibrated corrected output signal, which may then be utilized by othercircuitry.

FIG. 9 is a block diagram of an example of a fourth system forcorrecting DUT sigma-delta ADC 401, shown in a training configuration.In this embodiment, neural network 402 provides DUT sigma-delta ADC401's error only. Neural network 402 is trained by the differencebetween: (a) the output signal of DUT sigma-delta ADC 401 (i.e., withoutcompensation by neural network 402), as filtered by filter G 406 andtime-delayed by delay circuit 408, and (b) the output of filter F 409.This difference, labeled as the target signal, is then subtracted fromthe predicted error signal output from neural network 402 to produce anerror signal, which is processed through cost function 404 to trainneural network 402. Again, one or more PVT parameters 405 may beincorporated so that neural network 402 can further compensate theoutput of DUT sigma-delta ADC 401.

In some cases, the target signal may be provided by blocking thefundamental frequency with a bandpass filter, which provides the errorsignal directly, instead of subtracting the signal from filter F 409from the output of delay circuit 408. Depending on the analog inputsignal, such a filter may be band stop, low-pass (for very highfrequency input signals), bandpass, or high-pass (for very low frequencyinput signals).

A validation phase may be performed similarly as previously described,where an analog input signal is provided to DUT sigma-delta ADC 401 tocheck if the error is now sufficiently small or at least reduced for aset of exemplary inputs that DUT sigma-delta ADC 401 is likely toencounter. Where the training of ADCs is performed in a single sampletraining process (i.e., not in batches of ADCs), the validation phasemay be omitted.

During an inference or production phase, components 404 and 408 may beremoved, component 409 may be replaced by a short circuit, and the sameconfiguration shown in FIG. 6 may be used. During this inference phase,an analog input signal is applied to DUT sigma-delta ADC 401, whichproduces a digital output signal that is then modified by trained neuralnetwork 402 to produce a compensated or calibrated corrected outputsignal, which may then be utilized by other circuitry.

Accordingly, in various systems and methods described herein, the use offilter G 106, 206, 306, and 406 reduces the out-of-band noise of a DUTsigma delta ADCs 101, 201, 301, and 401, respectively. The filteringprevents excessive noise folding in neural networks 102, 202, 302, and402, and it prevents the out-of-band quantization noise from interferingwith the learning process of neural networks 102, 202, 302, and 402. Inthat way, a post-compensation scheme for ADCs using neural networks ismade suitable for sigma delta modulators. Moreover, in some embodiments,systems and methods described herein may replace reference ADCs 103 and203 with digital filters F 309 and 409.

In some cases, coefficients needed for neural networks 102, 202, 302,and 402 may be determined in a simulation (e.g., MATLAB) offline usingmeasurement data. The analog input signal is not needed at the time ofdetermining the coefficients. Instead, it may be reconstructed from thedata itself. The neural network coefficients can be uploaded to theproduct during final test.

In accordance with embodiments of the present disclosure, the trainingand validation phases described herein with respect to FIGS. 1, 5, 8,and 9 may be performed in a way that the various components areimplemented on or off an IC. In a first example, a test chip of the DUTADC may be produced, and a pre-selected number of samples may bemeasured. With this data, a neural network may be trained in software.Next, the trained neural network (with fixed biases and weights)together with the DUT ADC may be implemented into a product (e.g., anIC). In a second example, the DUT ADCs, reference ADCs, and neuralnetworks may be all implemented on an IC, but the reference ADCs mayonly be used to train the neural networks and are powered down duringthe end-use application of the IC. In a third example, the DUT ADCs andthe neural networks may be implemented on an IC, but not the referenceADCs, which are mounted on a test board for the training and validationphases.

It will also be noted that each block of the block diagrams, andcombinations of blocks in the block diagrams can be implemented byspecial purpose hardware-based systems (e.g., which may include one ormore graphics processing units) that perform the specified operations oracts, or combinations of special purpose hardware and computerinstructions. For example, a module (e.g., neural networks 102, 202,302, and 402, and cost functions 104, 204, 304, and 404) may beimplemented as a hardware circuit including custom VLSI circuits or gatearrays, off-the-shelf semiconductors such as logic chips, transistors,controllers, or other discrete components. Such a module may also beimplemented in programmable hardware devices such as field programmablegate arrays, programmable array logic, programmable logic devices,application specific ICs, microcontrollers, systems on a chip, generalpurpose processors, microprocessors, or the like.

Computer program code (i.e., instructions, for carrying out operations)may be written in any combination of one or more programming languages,including an object-oriented programming language such as Java,Smalltalk, Python, C++, or the like, conventional procedural programminglanguages, such as the “C” programming language or similar programminglanguages, or any of machine learning software.

These program instructions may also be stored in a computer readablestorage medium that can direct a computer system, other programmabledata processing apparatus, controller, or other devices to operate in aparticular manner, such that the instructions stored in the computerreadable medium produce an article of manufacture including instructionswhich implement the operations specified in the block diagram block orblocks.

The program instructions may also be loaded onto a computer, otherprogrammable data processing apparatus, controller, or other devices tocause a series of operations to be performed on the computer, or otherprogrammable apparatus or devices, to produce a computer implementedprocess such that the instructions upon execution provide processes forimplementing the operations specified in the block diagram block orblocks.

Reference is made herein to “configuring” a device or a device“configured to” perform some operation(s). It should be understood thatthis may include selecting predefined logic blocks and logicallyassociating them. It may also include programming computersoftware-based logic of a retrofit control device, wiring discretehardware components, or a combination of thereof. Such configureddevices are physically designed to perform the specified operation(s).

Modules implemented in software for execution by various types ofprocessors may, for instance, include one or more physical or logicalblocks of computer instructions, which may, for instance, be organizedas an object or procedure. Nevertheless, the executables of anidentified module need not be physically located together but mayinclude disparate instructions stored in different locations which, whenjoined logically together, include the module and achieve the statedpurpose for the module. Indeed, a module of executable code may be asingle instruction, or many instructions, and may even be distributedover several different code segments, among different programs, andacross several memory devices. Similarly, operational data (e.g.,knowledge bases of adapted weights and/or biases described herein) maybe identified and illustrated herein within modules and may be embodiedin any suitable form and organized within any suitable type of datastructure. The operational data may be collected as a single data set ormay be distributed over different locations including over differentstorage devices.

Systems and methods for correction of sigma-delta ADCs using neuralnetworks are described. In an illustrative, non-limiting embodiment, adevice may include: an ADC; a filter coupled to the ADC, where thefilter is configured to receive an output from the ADC and to produce afiltered output; and a neural network coupled to the filter, where theneural network is configured to receive the filtered output and toproduce a corrected output.

In some implementations, the ADC may include a delta-sigma ADC. The maybe configured to reduce out-of-band frequency content of the output. Theneural network may be configured to receive a PVT parameter and toproduce the corrected output based, at least in part, upon the PVTparameter.

The device may also include: a reference ADC configured to receive ananalog input provided to the ADC and to produce a target output; andanother filter coupled to the reference ADC, where the other filter isconfigured to receive the target output and to produce a filtered targetoutput. To produce the corrected output, the neural network may betrained with a difference between corrected outputs and filtered targetoutputs.

The device may further include: a delay circuit coupled between thefilter and the neural network, wherein the delay circuit is configuredto apply a time delay to the filtered output; and another filter coupledbetween the filter and the delay circuit, where the other filter isconfigured to receive the filtered output and to produce a targetoutput, and where the time delay is configured to synchronize thefiltered output with the target output.

The filter may be configured to reduce quantization noise of the output,and the other filter may be configured to reduce harmonic distortion ofthe filtered output. To produce the corrected output, the neural networkmay be trained with a difference between corrected outputs and targetoutputs.

In another illustrative, non-limiting embodiment, a device may include:an ADC; a filter coupled to the ADC, wherein the filter is configured toreceive an output from the ADC and to produce a filtered output; and aneural network coupled to the filter, where the neural network isconfigured to receive the filtered output and to predict an error that,subtracted from the filtered output, produces a corrected output.

In some implementations, the ADC may include a delta-sigma ADC. Thefilter may be configured to remove out-of-band frequency content of theoutput. The neural network may be further configured to receive adigital representation of a PVT parameter and to predict the errorbased, at least in part, upon the digital representation of the PVTparameter.

The device may also include another filter coupled to a digitalrepresentation of a reference ADC output, wherein the other filter isconfigured to receive the digital representation of the reference ADCoutput and to produce an intermediate output, and wherein theintermediate output subtracted from the filtered output produces atarget output. To predict the error, the neural network may be trainedwith a difference between predicted errors and target outputs.

The device may further include: a delay circuit coupled between thefilter and the neural network, where the delay circuit is configured toapply a time delay to the filtered output to produce a delayed, filteredoutput; and another filter coupled between the filter and the delaycircuit, where the other filter is configured to receive the filteredoutput and to produce an intermediate output, where the intermediateoutput subtracted from the delayed, filtered output produces a targetoutput, and where the time delay is configured to synchronize thedelayed, filtered output with the target output.

The filter may be configured to reduce quantization noise of the output,and the other filter may be configured to reduce harmonic distortion ofthe filtered output. To predict the error, the neural network may betrained with a difference between predicted errors and target outputs.

In yet another illustrative, non-limiting embodiment, a method mayinclude: receiving an analog input at an ADC; and producing a digitaloutput by the ADC, where the ADC is coupled to a neural network via afilter, where the filter is configured to reduce out-of-band frequencycontent of the digital output, and where the neural network isconfigured to produce at least one of: (a) a corrected digital output;or (b) a predicted error. In some implementations, the ADC may include adelta-sigma ADC.

In many implementations, systems and methods described herein may beincorporated into a wide range of electronic devices including, forexample, computer systems or Information Technology (IT) products suchas servers, desktops, laptops, memories, switches, routers, etc.;telecommunications hardware; consumer devices or appliances such asmobile phones, tablets, wearable devices, IoT devices, television sets,cameras, sound systems, etc.; scientific instrumentation; industrialrobotics; medical or laboratory electronics such as imaging, diagnostic,or therapeutic equipment, etc.; transportation vehicles such asautomobiles, buses, trucks, trains, watercraft, aircraft, etc.; militaryequipment, etc. More generally, these systems and methods may beincorporated into any device or system having one or more electronicparts or components.

Although the invention(s) is/are described herein with reference tospecific embodiments, various modifications and changes can be madewithout departing from the scope of the present invention(s), as setforth in the claims below. Accordingly, the specification and figuresare to be regarded in an illustrative rather than a restrictive sense,and all such modifications are intended to be included within the scopeof the present invention(s). Any benefits, advantages, or solutions toproblems that are described herein with regard to specific embodimentsare not intended to be construed as a critical, required, or essentialfeature or element of any or all the claims.

Unless stated otherwise, terms such as “first” and “second” are used toarbitrarily distinguish between the elements such terms describe. Thus,these terms are not necessarily intended to indicate temporal or otherprioritization of such elements. The terms “coupled” or “operablycoupled” are defined as connected, although not necessarily directly,and not necessarily mechanically. The terms “a” and “an” are defined asone or more unless stated otherwise. The terms “comprise” (and any formof comprise, such as “comprises” and “comprising”), “have” (and any formof have, such as “has” and “having”), “include” (and any form ofinclude, such as “includes” and “including”) and “contain” (and any formof contain, such as “contains” and “containing”) are open-ended linkingverbs. As a result, a system, device, or apparatus that “comprises,”“has,” “includes” or “contains” one or more elements possesses those oneor more elements but is not limited to possessing only those one or moreelements. Similarly, a method or process that “comprises,” “has,”“includes” or “contains” one or more operations possesses those one ormore operations but is not limited to possessing only those one or moreoperations.

1. A device, comprising: an analog-to-digital converter (ADC); a filtercoupled to the ADC, wherein the filter is configured to receive anoutput from the ADC and to produce a filtered output; and a neuralnetwork coupled to the filter, wherein the neural network is configuredto receive the filtered output and to produce a corrected output.
 2. Thedevice of claim 1, wherein the ADC comprises a delta-sigma ADC.
 3. Thedevice of claim 1, wherein the filter is configured to reduceout-of-band frequency content of the output.
 4. The device of claim 1,wherein the neural network is further configured to receive aProcess-Voltage-Temperature (PVT) parameter and to produce the correctedoutput based, at least in part, upon the PVT parameter.
 5. The device ofclaim 1, further comprising: a reference ADC configured to receive ananalog input provided to the ADC and to produce a target output; andanother filter coupled to the reference ADC, wherein the other filter isconfigured to receive the target output and to produce a filtered targetoutput.
 6. The device of claim 5, wherein to produce the correctedoutput, the neural network is trained with a difference betweencorrected outputs and filtered target outputs.
 7. The device of claim 1,further comprising: a delay circuit coupled between the filter and theneural network, wherein the delay circuit is configured to apply a timedelay to the filtered output; and another filter coupled between thefilter and the delay circuit, wherein the other filter is configured toreceive the filtered output and to produce a target output, and whereinthe time delay is configured to synchronize the filtered output with thetarget output.
 8. The device of claim 7, wherein the filter isconfigured to reduce quantization noise of the output, and wherein theother filter is configured to reduce harmonic distortion of the filteredoutput.
 9. The device of claim 7, wherein to produce the correctedoutput, the neural network is trained with a difference betweencorrected outputs and target outputs.
 10. A device, comprising: ananalog-to-digital converter (ADC); a filter coupled to the ADC, whereinthe filter is configured to receive an output from the ADC and toproduce a filtered output; and a neural network coupled to the filter,wherein the neural network is configured to receive the filtered outputand to predict an error that, subtracted from the filtered output,produces a corrected output.
 11. The device of claim 10, wherein the ADCcomprises a delta-sigma ADC.
 12. The device of claim 10, wherein thefilter is configured to remove out-of-band frequency content of theoutput.
 13. The device of claim 10, wherein the neural network isfurther configured to receive a digital representation of aProcess-Voltage-Temperature (PVT) parameter and to predict the errorbased, at least in part, upon the digital representation of the PVTparameter.
 14. The device of claim 10, further comprising another filtercoupled to a digital representation of a reference ADC output, whereinthe other filter is configured to receive the digital representation ofthe reference ADC output and to produce an intermediate output, andwherein the intermediate output subtracted from the filtered outputproduces a target output.
 15. The device of claim 14, wherein to predictthe error, the neural network is trained with a difference betweenpredicted errors and target outputs.
 16. The device of claim 10, furthercomprising: a delay circuit coupled between the filter and the neuralnetwork, wherein the delay circuit is configured to apply a time delayto the filtered output to produce a delayed, filtered output; andanother filter coupled between the filter and the delay circuit, whereinthe other filter is configured to receive the filtered output and toproduce an intermediate output, wherein the intermediate outputsubtracted from the delayed, filtered output produces a target output,and wherein the time delay is configured to synchronize the delayed,filtered output with the target output.
 17. The device of claim 16,wherein the filter is configured to reduce quantization noise of theoutput, and wherein the other filter is configured to reduce harmonicdistortion of the filtered output.
 18. The device of claim 16, whereinto predict the error, the neural network is trained with a differencebetween predicted errors and target outputs.
 19. A method, comprising:receiving an analog input at an analog-to-digital converter (ADC); andproducing a digital output by the ADC, wherein the ADC is coupled to aneural network via a filter, wherein the filter is configured to reduceout-of-band frequency content of the digital output, and wherein theneural network is configured to produce at least one of: (a) a correcteddigital output; or (b) a predicted error.
 20. The method of claim 19,wherein the ADC comprises a delta-sigma ADC.